Pore to continuum upscaling of permeability in heterogeneous porous media using mortars

Sun, Tie; Mehmani, Yashar; Bhagmane, Jaideep Shivaprasad; Balhoff, Matthew T.

doi:10.1504/ijogct.2012.046323

Cited by 28 publications

(18 citation statements)

References 26 publications

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“…“Hybrid multiscale multiphysics” methods are one approach to address problems that cannot be homogenized, and there has been increased interest in these methods in the porous media literature in recent years [ Balhoff et al ., ; Tartakovsky et al ., ; Battiato and Tartakovsky , ; Mehmani et al ., ; Sun et al ., ; Roubinet and Tartakovsky , ; Scheibe et al ., ]. For cases involving reaction fronts in localized portions of the domain, spatial domain decomposition can be considered.…”

Section: Introductionmentioning

confidence: 99%

“…[]. Among the methods reviewed, three are most relevant to this work: a weighted residual method based on mortar spaces [ Balhoff et al ., ; Mehmani et al ., ; Sun et al ., ], an iterative approach with a “handshake” domain [ Battiato et al ., ], and a semianalytical coupling technique that involves numerical solution of a global system of discretized equations that includes both domains [ Roubinet and Tartakovsky , ]. The mortar method utilizes a finite element space of reduced dimension and a Lagrange multiplier approach to compute matching boundary conditions for the adjacent pore‐scale and continuum‐scale regions in which computations are simultaneously performed [ Arbogast et al ., ; Peszynska et al ., ].…”

Section: Introductionmentioning

confidence: 99%

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A hybrid pore‐scale and continuum‐scale model for solute diffusion, reaction, and biofilm development in porous media

Tang

Valocchi

Werth

2015

Water Resources Research

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It is a challenge to upscale solute transport in porous media for multispecies bio-kinetic reactions because of incomplete mixing within the elementary volume and because biofilm growth can change porosity and affect pore-scale flow and diffusion. To address this challenge, we present a hybrid model that couples pore-scale subdomains to continuum-scale subdomains. While the pore-scale subdomains involving significant biofilm growth and reaction are simulated using pore-scale equations, the other subdomains are simulated using continuum-scale equations to save computational time. The pore-scale and continuumscale subdomains are coupled using a mortar method to ensure continuity of solute concentration and flux at the interfaces. We present results for a simplified two-dimensional system, neglect advection, and use dual Monod kinetics for solute utilization and biofilm growth. The results based on the hybrid model are consistent with the results based on a pore-scale model for three test cases that cover a wide range of Damk€ ohler (Da 5 reaction rate/diffusion rate) numbers for both homogeneous (spatially periodic) and heterogeneous pore structures. We compare results from the hybrid method with an upscaled continuum model and show that the latter is valid only for cases of small Damk€ ohler numbers, consistent with other results reported in the literature.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A hybrid pore‐scale and continuum‐scale model for solute diffusion, reaction, and biofilm development in porous media

Tang

Valocchi

Werth

2015

Water Resources Research

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“…Mortars are fi nite-element function spaces that ensure the (weak) continuity of fl ux at the interface between two coupled models (e.g., pore-scale and continuum-scale), and are the essential component of a highly fl exible, effi cient, and accurate non-overlapping domain decomposition method (Bernardi et al 1994;Arbogast et al 2000;Peszynska et al 2002). Subsequently, Sun et al (2012a) showed that mortars can be used as accurate upscaling tools for pore-scale models in obtaining macroscopic properties (e.g., permeability). They demonstrated that a large heterogeneous pore-scale domain can be decomposed along structural discontinuities and coupled via mortars to closely approximate the true permeability.…”

Section: Hybrid Modelingmentioning

confidence: 99%

Mesoscale and Hybrid Models of Fluid Flow and Solute Transport

Mehmani¹,

Balhoff²

2015

Reviews in Mineralogy and Geochemistry

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“…Theoretically, it would even be possible to couple pore-scale modelling with multiscale methods to upscale pore-scale physics directly to the reservoir scale (e.g. Sun et al 2012).…”

Section: Selected Advancesmentioning

confidence: 99%

Fundamental controls on fluid flow in carbonates: current workflows to emerging technologies

Agar

Geiger

2014

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The introduction reviews topics relevant to the fundamental controls on fluid flow in carbonate reservoirs and to the prediction of reservoir performance. The review provides research and industry contexts for papers in this volume only. A discussion of global context and frameworks emphasizes the value yet to be captured from compare and contrast studies. Multidisciplinary efforts highlight the importance of greater integration of sedimentology, diagenesis and structural geology. Developments in analytical and experimental methods, stimulated by advances in the materials sciences, support new insights into fundamental (pore-scale) processes in carbonate rocks. Subsurface imaging methods relevant to the delineation of heterogeneities in carbonates highlight techniques that serve to decrease the gap between seismically resolvable features and well-scale measurements. Methods to fuse geological information across scales are advancing through multiscale integration and proxies. A surge in computational power over the last two decades has been accompanied by developments in computational methods and algorithms. Developments related to visualization and data interaction support stronger geoscience-engineering collaborations. High-resolution and real-time monitoring of the subsurface are driving novel sensing capabilities and growing interest in data mining and analytics. Together, these offer an exciting opportunity to learn more about the fundamental fluid-flow processes in carbonate reservoirs at the interwell scale.

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Pore to continuum upscaling of permeability in heterogeneous porous media using mortars

Cited by 28 publications

References 26 publications

A hybrid pore‐scale and continuum‐scale model for solute diffusion, reaction, and biofilm development in porous media

A hybrid pore‐scale and continuum‐scale model for solute diffusion, reaction, and biofilm development in porous media

Mesoscale and Hybrid Models of Fluid Flow and Solute Transport

Fundamental controls on fluid flow in carbonates: current workflows to emerging technologies

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